Complementary Angles :
If the sum of two angles is 90⁰, then those two angles are called as complementary angles.
Example :
30° and 60° are complementary angles.
Because,
30° + 60° = 90°
Clearly, 30° is the complement of 60° and 60° is the complement of 30°.
Supplementary Angles :
If the sum of two angles is 180⁰, then those two angles are called as supplementary angles.
Example :
120° and 60° are supplementary angles.
Because,
120° + 60° = 180°
Clearly, 120° is the supplement of 60° and 60° is the supplement of 120°.
Question 1 :
The measure of an angle is 41°. What is the measure of a complementary angle?
Answer :
Let x be the measure of the required complementary angle.
Because x and 41° are complementary angles,
x + 41° = 90°
Subtract 41° from each side.
x = 49°
So, the measure of the complementary angle is 49°.
Question 2 :
The measure of an angle is 62°. What is the measure of a complementary angle?
Answer :
Let x be the measure of the required complementary angle.
Because x and 62° are complementary angles,
x + 62° = 90°
Subtract 62° from each side.
x = 28°
So, the measure of the complementary angle is 28°.
Question 3 :
The measure of an angle is 108°. What is the measure of a supplementary angle?
Answer :
Let x be the measure of the required supplementary angle.
Because x and 108° are supplementary angles,
x + 108° = 180°
Subtract 108° from each side.
x = 72°
So, the measure of the supplementary angle is 72°.
Question 4 :
The measure of an angle is 89°. What is the measure of a supplementary angle?
Answer :
Let x be the measure of the required supplementary angle.
Because x and 41° are supplementary angles,
x + 89° = 180°
Subtract 89° from each side.
x = 91°
So, the measure of the supplementary angle is 91°.
Question 5 :
Two angles are complementary. If one of the angles is double the other angle, find the two angles.
Answer :
Let x be one of the angles.
Then the other angle is 2x.
Because x and 2x are complementary angles, we have
x + 2x = 90°
3x = 90
Divide each side by 3.
x = 30
2x = 2(30) = 60
So, the two angles are 30° and 60°.
Question 6 :
Two angles are complementary. If one angle is two times the sum of other angle and 3, find the two angles.
Answer :
Let x and y be the two angles which are complementary.
x + y = 90° ----(1)
Given : One angle is two times the sum of other angle and 3.
x = 2(y + 3)
x = 2y + 6 ----(2)
Now, substitute (2y + 6) for x in (1).
2y + 6 + y = 90
3y + 6 = 90
Subtract 6 from each side.
3y = 84
Divide each side by 3.
y = 28
Substitute 28 for y in (2).
x = 2(28) + 6
x = 56 + 6
x = 62
So, the two angles are 62° and 28°.
Question 7 :
Find the value of x :
Answer :
In the picture above, the angles x° and (2x)° are complementary.
x° + (2x)° = 90°
x + 2x = 90
3x = 90
Divide each side by 3.
x = 30
So, the value of x is 30.
Question 8 :
Find the value of x :
Answer :
In the picture above, the angles
(x + 1)°, (x - 1)° and (x + 3)°
are complementary.
(x + 1)° + (x - 1)° + (x + 3)° = 90°
(x + 1) + (x - 1) + (x + 3) = 90
x + 1 + x - 1 + x + 3 = 90
3x + 3 = 90
Subtract 3 from each side.
3x = 87
Divide each side by 3.
x = 29
So, the value of x is 29.
Question 9 :
Find the value of x :
Answer :
In the picture above, the angles (2x + 3)° and (x - 6)° are supplementary.
(2x + 3)° + (x - 6)° = 180°
2x + 3 + x - 6 = 180
3x - 3 = 180
Add 3 to each side.
3x = 183
Divide each side by 3.
x = 61
So, the value of x is 61.
Question 10 :
Find the value of x :
Answer :
In the picture above, the angles
(5x + 4)°, (x - 2)° and (3x + 7)°
are supplementary.
(5x + 4)° + (x - 2)° + (3x + 7)° = 180°
5x + 4 + x -2 + 3x + 7 = 180
9x + 9 = 180
Subtract 9 from each side.
9x = 171
Divide each side by 9.
x = 19
So, the value of x is 19.
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